Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If PEMDAS is followed without remembering that multiplication and division have the same weight, and addition and subtraction have the same weight. Doing multiplication before division, can give the wrong answer. So can doing addition before subtraction. Some grade school books teach this incorrectly. For example: 6÷2×3 = 9, not 1. 6-2+3 = 7, not 1.

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations.

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 &#8722; 4 = 3 + (&#8722;4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 - 2 + 3 as the sum of 1, negative 2, and 3, and add in any order: (1 - 2) + 3 = -1 + 3 = 2 and in reverse order (3 - 2) + 1 = 1 + 1 = 2. The important thing is to keep the negative sign with the 2.

The root symbol, &#8730;, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand.

Stacked exponents are applied from the top down.

Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws.

1 or 9, depending on your country. In Russia it is 9. Because in Russia dividing and multiplaying are of the same level and being solved left to right. Fortunately we do not have a confusing PEMDAS...

Quoting: Anonymous Coward 1306057

This. We didn't have PEMDAS either in the USA when I went to school.

In a respectable setting, it would be clarified with parens whether one does the multiplication before the division (since there's a bias toward that), or works left to right and therefore the reverse in this case.

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations.

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 &#8722; 4 = 3 + (&#8722;4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 - 2 + 3 as the sum of 1, negative 2, and 3, and add in any order: (1 - 2) + 3 = -1 + 3 = 2 and in reverse order (3 - 2) + 1 = 1 + 1 = 2. The important thing is to keep the negative sign with the 2.

The root symbol, &#8730;, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand.

Stacked exponents are applied from the top down.

Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws.

Quoting: Anonymous Coward 1304583

Fascinating. Wikipedia <3

So where does it say I should put the denominator 2(1+2) up there with the numerator 6?

All around me are familiar faces... Worn out places...Worn out faces...

Side*note: A lot of you are relying on technology but inputting the equation incorrectly.

Quoting: Syrius

What the OP is telling you is the problem actually creates a FRACTION! A FRACTION has two parts the NUMERATOR and DENOMINATOR! Each part is dealt with on an individual basis not as a whole! Then you solve the problem! You calculator/computer tards don't even realize this is happening to you! THE ANSWER IS 1!

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations.

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 &#8722; 4 = 3 + (&#8722;4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 - 2 + 3 as the sum of 1, negative 2, and 3, and add in any order: (1 - 2) + 3 = -1 + 3 = 2 and in reverse order (3 - 2) + 1 = 1 + 1 = 2. The important thing is to keep the negative sign with the 2.

The root symbol, &#8730;, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand.

Stacked exponents are applied from the top down.

Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws.

Quoting: Anonymous Coward 1304583

Fascinating. Wikipedia <3

So where does it say I should put the denominator 2(1+2) up there with the numerator 6?

Quoting: Syrius

Syrius, using the mult inverse is simply a more complicated method for solving a very simple problem. The answer either way is 1!

Side*note: A lot of you are relying on technology but inputting the equation incorrectly.

Quoting: Syrius

What the OP is telling you is the problem actually creates a FRACTION! A FRACTION has two parts the NUMERATOR and DENOMINATOR! Each part is dealt with on an individual basis not as a whole! Then you solve the problem! You calculator/computer tards don't even realize this is happening to you! THE ANSWER IS 1!

Quoting: ANNONYMOUS 1275893

ITS FUCKING 9 DAMMIT, GET YOUR HEADS OUT OF YOUR ASSES

The (1+2) is done first inside the paranthesis. The outside division of 6 / 2 is done on its own second. Then the answer to the 6/2, which is 3 is then multiplied by the (3) giving you 9. Done and done and done...

Syrius, using the mult inverse is simply a more complicated method for solving a very simple problem. The answer either way is 1!

Quoting: ANNONYMOUS 1275893

I thought so to at first but forgot that multiplication and division are at the same level, in which case you MUST work left to right.

A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first. If you're not sure of this, test it in your calculator, which has been programmed with the Order of Operations hierarchy.